Overview
- Discusses J. Lambek’s groundbreaking works in mathematics, logic, linguistics, and theoretical computer science
- Surveys the fundamental influence of Lambek’s methods in algebra, proof theory, and computability
- Explores Lambek’s seminal ideas on linear logics, vector space models of grammar, and categorical models of language
Part of the book series: Outstanding Contributions to Logic (OCTR, volume 20)
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Table of contents (11 chapters)
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Front Matter
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Back Matter
Keywords
- Category theory and Algebra
- Categorical Proof Theory and Coherence
- Monoidal and Mal’cev Categories
- Sheaf Representation and Duality
- Categorical Recursion Theory
- Lambda Calculi and Dependent Types
- Noncommutative Linear Logics, Pomset logics, and Proof Nets
- Lambek Grammars and their extensions
- Lambek’s Pregroup models of linguistics
- Noncommutative Variants of Linear Logic
- Laws and Proof-Nets
- Sheaf Representations and Duality in Logic
- naturalness of Maltsev categories
- Extensions of Lambek Calculi
- Mathematics of Text Structure
- Pomset logic
- Categorical Recursion Theory
- Morphisms of Rings
- Pregroup Grammars, their Syntax and Semantics
- Sequent Calculus of Skew Monoidal Categories
About this book
This book is dedicated to the life and work of the mathematician Joachim Lambek (1922–2014). The editors gather together noted experts to discuss the state of the art of various of Lambek’s works in logic, category theory, and linguistics and to celebrate his contributions to those areas over the course of his multifaceted career.
After early work in combinatorics and elementary number theory, Lambek became a distinguished algebraist (notably in ring theory). In the 1960s, he began to work in category theory, categorical algebra, logic, proof theory, and foundations of computability. In a parallel development, beginning in the late 1950s and for the rest of his career, Lambek also worked extensively in mathematical linguistics and computational approaches to natural languages. He and his collaborators perfected production and type grammars for numerous natural languages. Lambek grammars form an early noncommutative precursor to Girard’s linear logic. In a surprising development (2000), he introduced a novel and deeper algebraic framework (which he called pregroup grammars) for analyzing natural language, along with algebraic, higher category, and proof-theoretic semantics.
This book is of interest to mathematicians, logicians, linguists, and computer scientists.
Editors and Affiliations
About the editors
Philip Scott is Emeritus Full Professor, Department of Mathematics and Statistics, University of Ottawa. His interests include categorical logic and algebra, proof theory, linear logic, and theoretical computer science. He is a senior editor of two major journals in these areas. He was a long-time collaborator of J. Lambek and the co-author of their well-known book Introduction to Higher Order Categorical Logic (1986).
Bibliographic Information
Book Title: Joachim Lambek: The Interplay of Mathematics, Logic, and Linguistics
Editors: Claudia Casadio, Philip J. Scott
Series Title: Outstanding Contributions to Logic
DOI: https://doi.org/10.1007/978-3-030-66545-6
Publisher: Springer Cham
eBook Packages: Religion and Philosophy, Philosophy and Religion (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
Hardcover ISBN: 978-3-030-66544-9Published: 21 March 2021
Softcover ISBN: 978-3-030-66547-0Published: 21 March 2022
eBook ISBN: 978-3-030-66545-6Published: 20 March 2021
Series ISSN: 2211-2758
Series E-ISSN: 2211-2766
Edition Number: 1
Number of Pages: XXXII, 432
Number of Illustrations: 1 b/w illustrations
Topics: Logic, Philosophy, general, Linguistics, general, Mathematical Logic and Foundations